Problem

Asia wants to buy a container that will hold the most gum balls. Container $\mathrm{A}$ is a cylinder with a height of $28.2 \mathrm{~cm}$ and a diameter of $9.6 \mathrm{~cm}$. Container B is a sphere that has a radius of $12.8 \mathrm{~cm}$. Which container will hold the most skittles? Approximate pi to 3.14 .

Answer

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Answer

Final Answer: The container that will hold the most skittles is \(\boxed{\text{Container B}}\).

Steps

Step 1 :Given that Container A is a cylinder with a height of 28.2 cm and a diameter of 9.6 cm, we can calculate its volume using the formula for the volume of a cylinder, \(\pi r^2 h\). The radius of the cylinder is half of the diameter, so it is 4.8 cm.

Step 2 :Substituting these values into the formula, we get \(\pi \times (4.8)^2 \times 28.2\), which equals approximately 2041.18 cubic cm.

Step 3 :Container B is a sphere with a radius of 12.8 cm. We can calculate its volume using the formula for the volume of a sphere, \(\frac{4}{3} \pi r^3\).

Step 4 :Substituting the given radius into the formula, we get \(\frac{4}{3} \pi \times (12.8)^3\), which equals approximately 8784.53 cubic cm.

Step 5 :Comparing the volumes of the two containers, we see that Container B has a larger volume than Container A.

Step 6 :Final Answer: The container that will hold the most skittles is \(\boxed{\text{Container B}}\).

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